However, in the calculation above we have ignored the fact that populations are structured, i.e. individuals any where in the world are not equally likely to be

However, in the calculation above we have ignored the fact that populations are structured, i.e. individuals any where in the world are not equally likely to be your parents. This means going back a few generations in the past individuals in your geographic area may be your ancestors, but individuals in geographically remote areas may likely not be. This means that while in a well mixed population (where individuals) move around a lot the above result will hold, in populations where migration is geographically limited it may take far longer for you to be descended from everyone (who left any descendants). However, some individuals within populations do migrate, and so some individuals in the population will have an ancestor in some distant geographic location in the previous generation. You only need to trace part of your family tree back to one of these migrant individuals in order for you to start having ancestors at geographically distant locations. Given the vast numbers of ancestors you have only a small number of generations back, it is quite likely that you trace your ancestry back to many different migrant ancestors. In turn these migrant ancestors quickly themselves have many ancestors further back in time, and so your ancestry quickly spreads around the world. Indeed Rhoades, Olsen, and Chang (2004) estimated under some fairly conservative assumptions about human migration that you might well trace your ancestry to everyone in the the entire world (who left descendants) may be just ~three thousand years ago. See http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-Article.pdf http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/Nature...